An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained from an approximation to the truncation terms of the governing equations. This approximation is calculated from the discrete nodal differential residuals using a reconstructed solution field on a modified stencil of points. Both the error estimation methodology and the flow solution scheme are implemented using the Finite Point Method, a meshless technique enabling higher-order approximations and reconstruction procedures on general unstructured discretizations. The performance of the proposed error indicator is studied and applications to adaptive grid refinement are presented.

The paper reports the results of suction controlled triaxial tests performed on compacted samples of two well graded granular materials in the range of coarse sand-medium gravel particle sizes: a quartzitic slate and a hard limestone. The evolution of grain size distributions is discussed. Dilatancy rules were investigated. Dilatancy could be described in terms of stress ratio, plastic work input and average confining stress. The shape of the yield locus in a triaxial plane was established by different experimental techniques. Yielding loci in both types of lithology is well represented by approximate elliptic shapes whose major axis follows approximately the Ko line. Relative humidity was found to affect in a significant way the evolution of grain size distribution, the deviatoric stress-strain response and the dilatancy rules.

The final publication is available at Springer via http://dx.doi.org/10.1007/s11440-016-0437-9

The design and evaluation of parachute-payload systems is a technology field in which numerical analysis tools can make very important contributions. This work describes a new development from CIMNE in this area, a coupled fluid-structural solver for unsteady
simulations of ram-air type parachutes. For an efficient solution of the aerodynamic problem, an unsteady panel method has been chosen exploiting the fact that large areas of separated
flow are not expected under nominal flight conditions of ram-air parachutes. A dynamic explicit finite element solver is used for the structure. This approach yields a robust solution
even when highly non-linear effects due to large displacements and material response are present. An added benefit of the proposed aerodynamic and structural techniques is that they
can be easily parallelized for increased performance in multi-core and multi-CPU architectures. The main features of the computational tools are described and several numerical examples are provided to illustrate the performance and capabilities of the
technique.

Purpose
– The purpose of this paper is to describe a set of simple yet effective, numerical method for the design and evaluation of parachute-payload system. The developments include a coupled fluid-structural solver for unsteady simulations of ram-air type parachutes. The main features of the computational tools are described and several numerical examples are provided to illustrate the performance and capabilities of the technique.
Design/methodology/approach
– For an efficient solution of the aerodynamic problem, an unsteady panel method has been chosen exploiting the fact that large areas of separated flow are not expected under nominal flight conditions of ram-air parachutes. A dynamic explicit finite element solver is used for the structure. This approach yields a robust solution even when highly nonlinear effects due to large displacements and material response are present. The numerical results show considerable accuracy and robustness.
Findings
– A simple and effective numerical tool for the analysis of parachutes has been developed.
Originality/value
– An analysis code has been developed which addresses the needs of ram-air parachute designers. The software delivers reasonably accurate results in a short time using modest hardware. It can therefore assist the design process, which nowadays relies on empirical methods.

This work deals with the development and application of the Finite Point Method (FPM) to compressible aerodynamics problems. The research focuses mainly on investigating the capabilities of the meshless technique to address practical problems, one of the most outstanding issues in meshless methods.
The FPM spatial approximation is studied firstly, with emphasis on aspects of the methodology that can be improved to increase its robustness and accuracy. Suitable ranges for setting the relevant approximation parameters and the performance likely to be attained in practice are determined. An automatic procedure to adjust the approximation parameters is also proposed to simplify the application of the method, reducing problem- and user-dependence without affecting the flexibility of the meshless technique.
The discretization of the flow equations is carried out following wellestablished approaches, but drawing on the meshless character of the
methodology. In order to meet the requirements of practical applications, the procedures are designed and implemented placing emphasis on robustness and efficiency (a simplification of the basic FPM technique is proposed to this end). The flow solver is based on an upwind spatial discretization of the convective fluxes (using the approximate Riemann solver of Roe) and an explicit time integration scheme. Two additional artificial diffusion schemes are also proposed to suit those cases of study in which computational cost is a major concern. The performance of the flow solver is evaluated in order to determine the potential of the meshless approach. The accuracy, computational cost and parallel scalability of the method are studied in comparison with a conventional FEM-based technique.
Finally, practical applications and extensions of the flow solution scheme are presented. The examples provided are intended not only to show the
capabilities of the FPM, but also to exploit meshless advantages. Automatic hadaptive procedures, moving domain and fluid-structure interaction problems, as well as a preliminary approach to solve high-Reynolds viscous flows, are a sample of the topics explored.
All in all, the results obtained are satisfactorily accurate and competitive in terms of computational cost (if compared with a similar mesh-based
implementation). This indicates that meshless advantages can be exploited with efficiency and constitutes a good starting point towards more challenging applications.

In this work, the finite point method is applied to the solution of high-Reynolds compressible viscous flows. The aim is to explore this important field of applications focusing on two main aspects: the easiness and automation of the meshless discretization of viscous layers and the construction of a robust numerical approximation in the highly stretched clouds of points resulting in such domain areas. The flow solution scheme adopts an upwind-biased scheme to solve the averaged Navier-Stokes equations in conjunction with an algebraic turbulence model. The numerical applications presented involve different attached boundary layer flows and are intended to show the performance of the numerical technique. The results obtained are satisfactory and indicative of the possibilities to extend the present meshless technique to more complex flow problems. Copyright (c) 2014 John Wiley & Sons, Ltd.

In this paper, "finite point method" (FPM) is presented for modeling 2D shallow water flow problem. The method is based on the use of a weighted least-square approximation procedure, incorporating QR factorization and an iterative adjustment of local approximation parameters. The stabilization of the convective term in this present work is derived from the approximate Riemann solver proposed by Roe. The present method is shown to produce competitive accuracy in the comparisons with the analytical solutions and the well-known Galerkin characteristic-based split (CBS) algorithm.

A comparative assessment of the Finite Point Method (FPM) is presented. Using a wing-fuselage configuration under transonic inviscid flow conditions as reference test case, the performance of the FPM flow solver is compared with an equivalent edge-based Finite Element (FEM) implementation. Efficiency issues have discouraged practical application of meshless methods in the past. Thus, a simplification of the basic FPM technique is proposed in order to reduce the performance gap with respect to classical grid-based algorithms. A comparative evaluation of the accuracy, computational cost and parallel performance of the meshless implementation is carried out with the objective to assess the level of maturity of the technique and identify improvements still required to tackle practical applications. The results obtained show accuracy and performance of the core algorithm comparable to a conventional FEM implementation, thus removing a major obstacle for further developments of the FPM.

A finite point method for solving compressible flow problems involving moving boundaries and adaptivity is presented. The numerical methodology is based on an upwind-biased discretization of the Euler equations, written in arbitrary Lagrangian–Eulerian form and integrated in time by means of a dual-time steeping technique. In order to exploit the meshless potential of the method, a domain deformation approach based on the spring network analogy is implemented, and h-adaptivity is also employed in the computations. Typical movable boundary problems in transonic flow regime are solved to assess the performance of the proposed technique. In addition, an application to a fluid–structure interaction problem involving static aeroelasticity illustrates the capability of the method to deal with practical engineering analyses. The computational cost and multi-core performance of the proposed technique is also discussed through the examples provided.

The finite point method (FPM) is a meshless technique, which is based on both, a weighted least-squares numerical approximation on local clouds of points and a collocation technique which allows obtaining the discrete system of equations. The research work we present is part of a broader investigation into the capabilities of the FPM to deal with 3D applications concerning real compressible fluid flow problems. In the first part of this work, the upwind-biased scheme employed for solving the flow equations is described. Secondly, with the aim of exploiting the meshless capabilities, an h-adaptive methodology for 2D and 3D compressible flow calculations is developed. This adaptive technique applies a solution-based indicator in order to identify local clouds where new points should be inserted in or existing points could be safely removed from the computational domain. The flow solver and the adaptive procedure have been evaluated and the results are encouraging. Several numerical examples are provided in order to illustrate the good performance of the numerical methods presented.

Electronic version of an article published as "International journal for numerical methods in fluids", vol. 60, no 9, 2009, p. 937-971. DOI:10.1002/fld.1892